C-172 ENCOUNTERS INFLT ICING DURING A NIGHT OP XCOUNTRY TRAINING FLT.

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I WAS FLYING AS PIC AS AN IFR STUDENT; WITH MY INSTRUCTOR IN THE R SEAT. ENRTE AT 8000 FT FROM NASHVILLE; WE SAW THE CLOUD TOPS SLOWLY RISE FROM 6000-7000 FT ON UP TO 8000 FT MSL. WE ASKED FOR; AND WERE GIVEN; 10000 FT AS A CRUISING ALT. THE CLOUDS CONTINUED THEIR GENTLE UPSLOPE; AND WE BEGAN TO BRUSH THEM AGAIN. WE ASKED FOR 11000 FT; THEN LATER 12000 FT FROM ATC. AS WE BEGAN TO PENETRATE THE CLOUDS AT 12000 FT; WE BOTH NOTICED ICE (RIME) FORMING ON THE WING STRUTS. BY THE TIME WE WERE CLRED TO 8000 FT (TO ATTEMPT TO DSND OUT OF THE ICING ENVIRONMENT); WE WERE PICKING UP MODERATE RIME ICE. DSNDING TOWARD 8000 FT; WE NOTIFIED ATC THAT THE ICING WAS MODERATE TO SEVERE RIME; AND REQUESTED 3000 FT. UPON REACHING 3000 FT (AND LATER 2500 FT); OUR 1/2 INCH ICE ON THE WINGS FELL OFF GRADUALLY. CTL OF THE ACFT WAS NEVER LOST; NO REGULATIONS WERE BROKEN; AND NO HAZARD TO OURSELVES OR OTHER ACFT WAS EXPERIENCED. MY ACTIONS WERE CONSISTENT WITH PRESCRIBED ICING PROCS. NO ICING WAS FORECAST FOR THE AREA ENRTE; AND NO 'KNOWN ICING' WAS ENTERED.